Classes of the differential equations with small parametre of the elliptic type, containing special points of type of a saddle in the limiting equation are investigated. Asymptotic expansion of the solutions of boundary value problems convective diffusions about a particle are constructed. Theorems of existence are proved and asymptotic expansion of the solutions for some classes of the quasilinear ordinary differential equations arising in problems convective diffusion taking into account volumetric chemical reaction are constructed.
Main publications:
Rustyam G. Akhmetov and Ruslan R. Kutluev, “Vortex structure around the cylinder at a flow of viscous fluid”, APPLIED NONLINEAR DYNAMICAL SYSTEMS, 93, Proceedings in Mathematics and Statistics in Springer Series., 2014
N. V. Maksimova, R. G. Akhmetov, “The asymptotic solutions for boundary value problem to a convective diffusion equa-tion with chemical reaction near a cylinder”, Latin American Journal of Solids and Structures., 10 (2013), 123-131
Akhmetov R.G., “The asymptotic expansions of the solution for the boundary value problem to a convective diffusion equation with volume chemical reaction near a spherical drop”, Communications in Nonlinear Science and Numerical Simulation, 15 (2011), CNSNS 1577 , 2308-2312. pp.
R.G. Akhmetov, “Asymptotics of Solutions to a Singularly Perturbed Problem for the Diffusion Equation in a Neighborhood of a Saddle Point of the Limiting Operator”, Dokl. Akad. Nauk, 362 (1998), 727-728 (Dokl. Math. 58, 271-272 (1998).)
Rustyam G. Akhmetov, Ruslan R. Kutluev, “About the Structure of the Vortex Flow Around Cylinder With Viscous Fluid”, Journal of Applied Nonlinear Dynamics, 3:4 (2014), 307–315
